Which operation i.e a 32 bit operation or a 64 bit operation (like masking a 32 bit flag or a 64 bit flag), would be cheaper on a 64 bit machine?
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As you don;t specify an architecture, I can suggest only a general answer, as it depends on the operation and on the processor architecture in question. Once you have the data in a CPU register, then most operations will usually take the same amount of time regardless of whether the value was originally 32 or 64 bit.
However, there can be some differences on some architectures in how the data gets into a register. Here are some situations where a “native” value may be faster than a smaller value on some hardware:
Fetching data
Fetching a “native sized” value may be faster than fetching a smaller value. That is, the processor may need to fetch 64 bits regardless, and then mask/shift off 32 bits of it to “load” a 32-bit value. This masking/shifting is not required when working on a 64 bit value, so it can possibly be loaded faster. (This goes against the intuitive idea that something twice as big might take twice as long to load).
Alternatively, if the bus can handle half-width fetches, then 32 bits may be loaded in the same time as a 64 bit value.
To confuse matters more, the CPU caches can change results as well. Usually when you read one value from memory, a “line” of several memory locations are read into the cache, so that subsequent reads can be supplied from fast cache memory instead of requiring a full fetch from RAM. In which case using 32 bit values will work out faster if you are accessing many values in sequence, as twice as many of them will be cached, resulting in fewer cache misses.
Computation
the processor hardware is optimised for dealing with 64-bit values, so calculating values using 32 bits may cause it more trouble, and thus could slow things down. e.g. It might be able to process a double (64-bit) value “natively” but have to convert a float (32-bit) value into a double before it can process it, then convert the result back to a float afterwards.
Alternatively, there may be 32-bit and 64-bit paths through the CPU, or the CPU may be able to do any conversions required in a way that does not affect the overall execution time of the instruction, in which case they may be calculated at the same speed.
This may affect complex operations (floating point) but is unlikely to be a problem with simple ops (AND, OR, etc)